AuthorTopic: philosophy, politics, or economics major and law school success (Read 13146 times)

Friend or Foe?, did you name yourself after the game show Friend or Foe? on Game Show Network, by now off the air? I absolutely abhorred that show... I mean, look at the way the choices made by the contestants were fashioned to lead to:

Both vote "Friend" -- Each player received half the winnings. One votes "Friend," the other "Foe" -- The contestant voting "Foe" takes all the money. Both vote "Foe" -- Neither player wins anything.

[...] The notion that the Soviets tried to acquire nuclear superiority and in the process accelerated the demise of their economy is a Pyrrhic victory given the missile threat we still face, and the inevitable proliferation of nuclear weapons into unstable terrorists' hands.

Speaking of Pyrrhus, BTW, the whole Pyrrhus' life could be considered as a big seesaw. Once up and then down again!

Pyrrhus was the son of Aeacides of Epirus and Phthia, and a second cousin of Alexander the Great. Prince of one of the Alexandrian successor states, Pyrrhus' childhood and youth went by in unquiet conditions. He was only two years old when his father was dethroned and the family took refuge with Glaukias, king of the Taulanti, one of the largest Illyrian tribes. Later, the Epirotes called him back but he was dethroned again at the age of 17 when he left his kingdom to attend the wedding of Glaukias' son in Illyria. In the wars of the diadochi Pyrrhus fought beside his brother-in-law Demetrius I of Macedon on the losing side in the pivotal Battle of Ipsus (301 BC). Later, he was made a hostage of Ptolemy I Soter by a treaty between Ptolemy I and Demetrius. Pyrrhus married Ptolemy I's stepdaughter Antigone and in 297 BC, with Ptolemy I's aid, restored his kingdom of Epirus. Next he went to war against his former ally Demetrius. By 286 BC he had deposed his former brother-in-law and taken control over the kingdom of Macedon. Pyrrhus was driven out of Macedon by Lysimachus, his former ally, in 284 BC.

His name is famous for the phrase "Pyrrhic victory" which refers to an exchange at the Battle of Asculum. When Pyrrhus invaded Apulia (279 BC), the two armies met in the Battle of Asculum where Pyrrhus won a very costly victory. The consul Publius Decius Mus was the Roman commander, and his able force, though defeated, broke the back of Pyrrhus' Hellenistic army, and guaranteed the security of the city itself. The battle foreshadowed later Roman victories over more numerous and well armed successor state military forces and inspired the term "Pyrrhic victory", meaning a victory which comes at a crippling cost. At the end, the Romans had lost 6,000 men and Pyrrhus 3,500 but, while battered, his army was still a force to be reckoned with.

In 272 BC, Cleonymus, a Spartan of royal blood who was hated among fellow Spartans, asked Pyrrhus to attack Sparta and place him in power. Pyrrhus agreed to the plan intending to win control of the Peloponnese for himself but unexpectedly strong resistance thwarted his assault on Sparta. He was immediately offered an opportunity to intervene in a civic dispute in Argos. Entering the city with his army by stealth, he found himself caught in a confused battle in the narrow city streets. During the confusion an old Argead woman watching from a rooftop threw a roofing tile which stunned him, allowing an Argive soldier to kill him.

Friend or Foe?, did you name yourself after the game show Friend or Foe? on Game Show Network, by now off the air? I absolutely abhorred that show... I mean, look at the way the choices made by the contestants were fashioned to lead to:

Both vote "Friend" -- Each player received half the winnings. One votes "Friend," the other "Foe" -- The contestant voting "Foe" takes all the money. Both vote "Foe" -- Neither player wins anything.

Exactly the Prisoner's Dilemma combinations of choices

It's actually the same as the game of Chicken. It underscores the principle that while each player prefers not to yield to the other, the outcome where neither player yields is the worst possible one for both players. The name "Chicken" has its origins in a game in which two drivers drive towards each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves but the other does not, he or she will be called a "chicken." The game is similar to the prisoner's dilemma game in that an "agreeable" mutual solution is unstable since both players are individually tempted to stray from it. However, it differs in the cost of responding to such a deviation. This means that, even in an iterated version of the game, retaliation is ineffective, and a mixed strategy may be more appropriate.

The game models two drivers, both headed for a single lane bridge from opposite directions. The first to swerve away yields the bridge to the other. If neither player swerves, the result is a costly deadlock in the middle of the bridge, or a potentially fatal head-on collision. It is presumed that the best thing for each driver is to stay straight while the other swerves (since the other is the "chicken" while a crash is avoided). Additionally, a crash is presumed to be the worst outcome for both players. This yields a situation where each player, in attempting to secure his best outcome, risks the worst. A similar version, under the name of "chickie run", is a central plot element in the movie "Rebel Without a Cause" where the characters played by James Dean and Corey Allen race their cars towards a cliff instead of each other. The phrase game of Chicken is also used as a metaphor for a situation where two parties engage in a showdown where they have nothing to gain, and only pride stops them from backing down.

This yields a situation where each player, in attempting to secure his best outcome, risks the worst. A similar version, under the name of "chickie run", is a central plot element in the movie "Rebel Without a Cause" where the characters played by James Dean and Corey Allen race their cars towards a cliff instead of each other. The phrase game of Chicken is also used as a metaphor for a situation where two parties engage in a showdown where they have nothing to gain, and only pride stops them from backing down.

That's curious..

Logged

This next song doesn't go 'something' like this; it goes 'exactly' like this.

I was a poli sci major (useless), but took some interest in econ and philo, and that's the stuff I find to resonate the most in law school. The only thing that came in handy from poli sci was game theory.

Some time back I thought of an example which shed light for me on some of the fail-to-disagree results. Imagine that two players, A and B, are going to play a coin-guessing game. A coin is flipped out of sight of the two of them and they have to guess what it is. Each is privately given a hint about what the coin is, either heads or tails; and they are also told the hint "quality", a number from 0 to 1. A hint of quality 1 is perfect, and always matches the real coin value. A hint of quality 0 is useless, and is completely random and uncorrelated with the coin value. Further, each knows that the hint qualities are drawn from a uniform distribution from 0 to 1 - on the average, the hint quality is 0.5. The goal of the two players is to communicate and come up with the best guess as to the coin value. Now, if they can communicate freely, clearly their best strategy is to exchange their hint qualities and just follow the hint with the higher quality. However we will constrain them so they can't do that. Instead all they can do is to describe their best guess at what the coin is, either heads or tails. And further, we will divide their communication into rounds, where in each round the players simultaneously announce their guesses to each other. Upon hearing the other player's guess, each updates his own guess for the next round.

Read on below the break for some sample games to see how the players can resolve their disagreement even with such stringent constraints.

Here's a straightforward example where we will suppose A gets a hint with quality 0.8 of Heads, and B gets a hint with quality 0.6 of Tails. Initially the two sides tell each other their best guess, which is the same as their hint:

A:H B:T

Now they know they disagree. Their reasoning can be as follows:

A: B's hint quality is uniform in [0,1], averaging 0.5. My hint quality is higher than that at 0.8, so I will stay with Heads.B: A's hint quality is uniform in [0,1], averaging 0.5. My hint quality is higher than that at 0.6, so I will stay with Tails.

A:H B:T

So they remain unchanged. Now they reason:

A: B did not change, so his hint quality must be higher than 0.5. That is all I know, so it must be uniform in [0.5,1], averaging 0.75. My hint quality is higher than that at 0.8, so I will stay with Heads.B: A did not change, so his hint quality must be higher than 0.5, so it must be uniform in [0.5,1], averaging 0.75. My hint quality is lower than that at 0.6, so I will switch to Heads.

A:H B:H

And they have come to agreement. If both A and B had had higher hint qualities, they might have persisted in their disagreement for more rounds, but each refusal to switch tells the other party that their hint quality must be even higher, and eventually one side will give way. It's improbable that both sides will have high but opposite hint qualities. What happens in the more likely case where they have low but opposite hint qualities? Let's suppose that A gets a hint of Heads with quality 0.1, and B gets a hint of Tails with quality 0.15.

A:H B:T

A: B's hint quality is uniform in [0,1], averaging 0.5, which is higher than my 0.1, so I will switch to Tails.B: A's hint quality is uniform in [0,1], averaging 0.5, which is higher than my 0.15, so I will switch to Heads.

A:T B:H

A: B switched, so his hint quality was lower than 0.5, making it uniform in [0,0.5] and averaging 0.25, which is higher than my 0.1, so I will stay with Tails (B's original guess).B: A switched, so his hint quality was lower than 0.5, making it uniform in [0,0.5] and averaging 0.25, which is higher than my 0.1, so I will stay with Heads (A's original guess).

A:T B:H

A: B stayed the same, so his hint quality was lower than 0.25, making it uniform in [0,0.25] and averaging 0.125, which is higher than my 0.1, so I will stay with Tails.B: A stayed the same, so his hint quality was lower than 0.25, making it uniform in [0,0.25] and averaging 0.125, which is lower than my 0.15, so my original hint quality was higher, and I will switch back to my original Tails.

A:T B:T

Once again agreement is reached. Note that when both sides have a low hint quality, they initially switch to the other side's original view, then they each stick with that new side. After enough rounds one of them decides that the other's hint must have been so poor that his hint was better, and he switches back to reach agreement. An interesting case arises if the hint qualities are near 1/3 or 2/3. In that case we can get sequences like this (I will skip the reasoning, you can work it out if you like):

A:H B:T

A:T B:H

A:H B:T

A:T B:H

A:H B:H

Here we can have both sides changing back and forth potentially several times, each side taking the other's view, until they come to agreement.

A few interesting points about this game. It's a simple model that captures some of the flavor of the no-disagreement theorem. In the real world we have hints about reality in the form of our information; and there is something like a "hint quality" in terms of how good our information is. If we were Bayesians we could both report our hint qualities when we disagree, and go with the one that is higher. Even if we are limited merely to reporting our opinions as in this game, we should normally reach agreement pretty quickly. Another interesting aspect is that when you play the game, you can never anticipate your partner's guess. On each round you have an idea of the range of possible hint qualities he might have, based on his play so far, and it always turns out that given that range, he is equally likely to guess Heads or Tails on the next round. This is related to Robin's result that the course of opinions among Bayesians in resolving disagreement goes as a random walk.

As I noted, in the real world it should be uncommon for two people to have high quality but opposing hints, because high quality hints are supposed to be accurate. Hence it should be rare for people to stubbornly disagree and stick to their original viewpoints. Much more common should be the case where people have low quality hints which disagree. In that case, as we saw, people should switch position at least once, and then (depending on how low the hint quality was) either stick to their reversed position or else possibly alternate some more. This should be a common course of disputation between Bayesians, but it is strikingly rare among humans. Another point this game illustrates is that the Aumannian notion of "common knowledge" may not be as easy to use as it seems. Note in this game that even after announcing their positions, players' (current) views are not common knowledge. After each round, a player got new information that could have changed his view from when he stated it before. Once they reach agreement, then things seem to stabilize, but that may not be the case in general. I have constructed different games in which people can agree for two consecutive rounds and then disagree. It is an open question to me whether two people can agree for N rounds and then disagree, for arbitrary N.

Study anything that helps you comprehend dense material that must be parsed through quickly. Start practicing LSATs begining sr. year and figure out the logic game system. That's about it. Take LSAT get 161 or above and go to pretty decent school pretty much anywhere. That's about it. Majors irrelevant. More mathematical of a mind you have, the better you'll likely do on LSAT. That's all that matters. You could be be an underwater basket weaver major and if you do well on LSAT you're fine in law school.

this may sound outlandish but what about reading several books or articles to boost your rc? obviously i'm not talking about this to substitute intense lsat studying, but if you really want to improve your rc before law school would investing in some good reads--literature or non-fiction--do no good in improving your overall rc? i.e., scholarly journals; moral/philosophical papers; literature? which subject would be best for this, if at all? muchos gracias.